Drug distribution pharmacokinetic modeling

The use of distributed pharmacokinetic models to estimate expected concentration profiles associated with different modes of drug delivery requires that various input parameters be available. The most commonly required parameters, as seen in Equation 9.1, are diffusion coefficients, reaction rate constants, and capillary permeabilities. As will be encountered later, hydraulic conductivities are also needed when pressure-driven rather than diffusion-driven flows are involved. Diffusion coefficients (i.e., the De parameter described previously) can be measured experimentally or can be estimated by extrapolation from known values for reference substances. Diffusion constants in tissue are known to be proportional to their aqueous value, which in turn is approximately proportional to a power of the molecular weight. Hence,... 

Physiologically based pharmacokinetic models provide a format to analyze relationships between model parameters and physicochemical properties for a series of drug analogues. Quantitative structure-pharmacokinetic relationships based on PB-PK model parameters have been pursued [12,13] and may ultimately prove useful in the drug development process. In this venue, such relationships, through predictions of tissue distribution, could expedite drug design and discovery. 

D Shen, M Gibaldi. Critical evaluation of use of effective protein fractions in developing pharmacokinetic models for drug distribution. J Pharm Sci 63 1698-1702, 1974. 

Potential error in the measurement of tissue to blood distribution coefficients in physiological pharmacokinetic modeling residual tissue blood. 1. Theoretical considerations, Drug Metab. Dispos. 1991, 19, 478—485. 

Ward et al. [125] investigated the disposition of 14C-radiolabeled primaquine in the isolated perfused rat liver preparation, after the administration of 0.5, 1.5, and 5 mg doses of the drug. The pharmacokinetics of primaquine in the experimental model was dependent on dose size. Increasing the dose from 0.5 to 5 mg produced a significant reduction in clearance from 11.6 to 2.9 mL/min. This decrease was accompanied by a disproportionate increase in the value of the area under the curve from 25.4 to 1128.6 pg/mL, elimination half-life from 33.2 to 413 min, and volume of distribution from 547.7 to 1489 mL. Primaquine exhibited dose dependency in its pattern of metabolism. While the carboxylic acid derivative of primaquine was not detected perfusate after the 0.5 mg dose, it was the principal perfusate metabolite after 5 mg dose. Primaquine was subject to extensive biliary excretion at all doses, the total amount of 14C-radioactivity excreted in the bile decreased from 60 to 30%i as the dose of primaquine was increased from 0.5 to 5 mg. 

The importance of these equations is that drugs can have different half-lives due either to changes in clearance or changes in volume (see Section 2.7). This is illustrated in Figure 2.3 for a simple single compartment pharmacokinetic model where the half-life is doubled either by reducing clearance to 50 % or by doubling the volume of distribution. 

As with classic compartment pharmacokinetic models, PBPK models can be used to simulate drug plasma concentration versus time profiles. However, PBPK models differ from classic PK models in that they include separate compartments for tissues involved in absorption, distribution, metabolism and elimination connected by physiologically based descriptions of blood flow (Figure 10.1). 

Although Eq. (1) is a simple mathematical relationship, there are numerous limitations to its appropriate application, based on the assumptions one makes about the pharmacokinetic model to which it is applied. In the case where one assumes instantaneous equilibrium of drug between the tissue and the plasma or blood (i.e., a one-compartment model), the concentration in the sampling compartment is, by definition, proportional to the tissue concentration at all times after dosing, and V determined for any At and Ct pair will be constant Since At at time 0 is the dose (D), it is common to express volume of distribution in a one-compartment model as ... 

The administration of a drug by a rapid intravenous injection places the drug in the circulatory system where it is distributed (see section 2.7.1) to all the accessible body compartments and tissues. The one compartment model (Figure 8.3(a)) of drug distribution assumes that the administration and distribution of the drug in the plasma and associated tissues is instantaneous. This does not happen in practice and is one of the possible sources of error when using this model to analyse experimental pharmacokinetic data. 

Roberts MS, Donaldson JD, Rowland M. Models of hepatic elimination a comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity, and systemic recycling on hepatic elimination. J Pharmacokinet Biopharm 1988 16 41-83. 

The PPK approach estimates the joint distribution of population specific pharmacokinetic model parameters for a given drug. Fixed effect parameters quantify the relationship e.g. of clearance to individual physiology like function of liver, kidney, or heart. The volume of distribution is typically related to body size. Random effect parameters quantify the inter-subject variability which remains after the fixed effects have been taken into account. Then the observed concentrations will still be randomly distributed around the concentration time course predicted by the model for an individual subject. This last error term called residual variability... 

The distribution and disposition of a drug in the body result from a complex set of physiological processes and biochemical interactions. In principle, it is possible to describe these processes and interactions in mathematical terms and, if sufficient data are available, to predict the time course of drug and metabolite(s) in different species and at specific anatomic sites (15). A physiological pharmacokinetic model was developed to predict the deamination of cytosine arabinoside (ARA-C) in humans from enzyme parameters determined from homogenates of human tissue (16). ARA-C is converted to its inactive metabolite, uracil arabinoside (ARA-U) by cytidine deaminase, the activity of which varies substantially among tissues. 

Biophase Distribution Model. Drug distribution to the effect site may represent a rate-limiting step for drugs in exerting their pharmacological effect. Holford and Sheiner introduced a hypothetical effect-compartment (Fig. 7), and proposed that a drug must first enter this effect compartment from either the central or the peripheral pharmacokinetic compartment before its pharmacological response is exerted. ... 

Atkinson A J, Ruo T, Frederiksen M C 1996 Physiological basis of multicompartmental models of drug distribution. Trends in Pharmacological Sciences 12 96-101 Baggot J D 1990 Pharmacokinetic-pharmcodynamic relationship. Annals de Recherches Veterinaires 21(suppl) 29-40... 

When the dose of a drug is administered as an intravenous bolus, the volume of distribution at steady-state (Vd(ss)) can be calculated. This parameter represents the volume in which a drug would appear to be distributed during steady-state if the drug existed throughout that volume at the same concentration as in the measured fluid (plasma or blood). The volume of distribution at steady-state is generally calculated by a non-compartmental method, which is based on the use of areas (Benet Galeazzi, 1979) and does not require the application of a compartmental pharmacokinetic model or mathematical description of the disposition curve ... 

The advantages of using non-compartmental methods for calculating pharmacokinetic parameters, such as systemic clearance (CZg), volume of distribution (Vd(area))/ systemic availability (F) and mean residence time (MRT), are that they can be applied to any route of administration and do not entail the selection of a compartmental pharmacokinetic model. The important assumption made, however, is that the absorption and disposition processes for the drug being studied obey first-order (linear) pharmacokinetic behaviour. The first-order elimination rate constant (and half-life) of the drug can be calculated by regression analysis of the terminal four to six measured plasma... 

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